Perform the indicated matrix operations. If the matrix does not exist, write impossible.

$$-2\left[\begin{array}{rrrr}2 & 11 & -5 & 4 \\ -1 & 0 & 6 & 3 \\ 9 & -2 & 1 & 0\end{array}\right]$$

Fill in the Blank A curve in the coordinate plane is the graph of a function if and only if no.......... intersects it more than once.

Find solutions to the given initial value problem. \

$$y^{\prime \prime}+3 t y^{\prime}-6 y=1 ; \quad y(0)=0, \quad y^{\prime}(0)=0$$

Consider the eigenvalue problem

$$\begin{gathered} \nabla^2 \phi+\lambda \phi=0 \\ \frac{\partial \phi}{\partial x}(0, y)=0, \quad \phi(x, 0)=0 \\ \frac{\partial \phi}{\partial x}(L, y)=0, \quad \phi(x, H)=0 \end{gathered}$$

Show that the eigenfunctions are orthogonal in a two-dimensional sense using two one-dimensional orthogonality relations.

Evaluate each.factorial expression.

$$\frac { 11 ! } { ( 11 - 3 ) ! }$$

If points $A, B$, and $C$ on a coordinate line have coordinates $-8,4$, and $-3$, respectively, tind the distance:

$$d(A, C)$$

Solve.

Alex has a pair of red socks, a pair of white socks, and a pair of black socks in his drawer. Unfortunately, the socks are not matched up with each other. Alex reaches into the drawer in the dark and pulls out two socks.

(a) What is the probability that the two socks are the same color?

(b) What is the probability that the two socks are different colors?

($c$) Are the two events described in (a) and (b) complementary? Explain.

The equation of a conic section is given in a familiar form. Identify the type of graph that the equation has, without actually graphing.

$$y+7=4(x+3)^2$$

Solve the inequality. -4/11 z - 1 > -8/11

What are hieroglyphics?

What type of conic is given by $r=\frac{3}{2-0.5 \cos \theta}?$ F. circle G. ellipse H. parabola J. hyperbola

Develop Hypotheses A certain rock has large. crystals of feldspar, mica, and quartz. Explain how and where the rock might have formed.

Find the velocity, acceleration, and speed of a particle whose motion is along the space curve traced out by the vector function $\mathbf{r}=\mathbf{r}(t)$. $\mathbf{r}(t)=t \mathbf{i}+\sin (4 t) \mathbf{j}+\cos (4 t) \mathbf{k}$

Suppose that an object that is originally at room temperature of $32^{\circ} \mathrm{C}$ is placed in a freezer. The temperature T(x) (in $^{\circ} \mathrm{C}$) of the object can be approximated by the model

$$T(x)=\frac{320}{x^{2}+3 x+10}$$

where x is the time in hours after the object is placed in the freezer. a. What is the horizontal asymptote of the graph of this function and what does it represent in the context of this problem? b. A chemist needs a compound cooled to less than $5^{\circ} \mathrm{C}$. Determine the amount of time required for the compound to cool so that its temperature is less than $5^{\circ} \mathrm{C}$.